The “Golden Batch” or Iron Pyrite?
Some companies judge the status of batch processing by a standard set by the so-called “golden” or ideal batch. Typically, a golden batch is defined as the time-based profile of the measurement values that were recorded for a particular batch that met product quality targets. When using this standard, a batch is judged by how closely the golden batch profile is maintained though the adjustment of process inputs.
The term “golden batch” certainly has a nice sales and marketing ring to it, and many companies promote it. It is very easy to implement a comparative overlay of a current batch time-based profile with the single trace of the golden batch, and to the casual user, this approach may seem very logical. However, it is plagued with problems inherently.
The approach has two big weaknesses. First, conditions indicated by each measurement may affect product quality in a different manner. For example, it may be important to control some parameters tightly, while other measurements may vary significantly without affecting the product quality. Second, the “golden batch” is a univariate approach to a multivariate problem. There is absolutely no knowledge gained of the relationships of process variations. One simply emulates a single batch without knowing why, where or how this trajectory is good.
Without taking these and other key items into consideration, actions taken may incorrectly allocate resources, leading to incorrect control strategies. Time and money may be spent to improve control where it is not needed and directed away from where it is. Through the use of multivariate statistical techniques, it is possible to characterize variations both within and between batches and relate them to both process relationships and to predicting typical batch events and important end-of-batch quality characteristics.
One of the important multivariate statistical methods is principal component analysis (PCA). At the heart of PCA is the concept that a time-based profile for measurement values may be established using a variety of batches that produced good quality product and had no abnormal processing upsets. Analysis tools designed for batch analysis make it possible to extract, analyze and use data from multiple batches. For these batches, the normal variation in measurements is then quantified in terms of a PCA model. The model may then be used to develop a better understanding of how multivariate parameters relate to one another, and how these can affect the batch-to-batch costs, energy, waste and time needed to produce a product.
The model structure automatically takes into account that many of the measurements used in the batch operation are collinear; that is, related to each other and respond in a similar manner to a process input change. You can use the PCA model to identify process and measurement faults that may affect product quality. A problem is flagged only if a parameter deviates by more than the typical variation defined for a good product. As a result, the multivariable environment of a batch operation may be reduced to just a few simple statistics that the operator may use to assess how the batch is progressing. These statistics take into account the significance of a component’s variation from its established profile in predicting a fault.
Through the use of PCA, it is possible to detect abnormal operations resulting from both measured and unmeasured faults.
- Measured disturbances. The PCA model captures contributions of each process measurement to the normal process operation. Deviations in the process operation may be quantified through the application of Hotelling’s T2 statistic. Given an assigned level of significance, threshold values can be determined to detect an abnormal condition. The T2 statistic is a multivariable generalization of the Shewhart chart.
- Unmeasured disturbances. The portion of a process deviation that is not captured by the PCA model reflects changes in unmeasured disturbances. The Q statistic, also known as the squared prediction error (SPE), is a measure of deviations in process operation that are the results of unmeasured disturbances.
Through the use of these two statistics, it is possible for operators to determine fault conditions sooner in the batch, thus allowing corrections to be made to counter the impact of the fault.
Projection to latent structures (PLS)— also known as partial least squares— may be used to analyze the impact of processing conditions on final-product quality parameters. When this technique is applied in an online system, it can provide operators with continuous prediction of end-of-batch quality parameters. Where the objective is to classify the operation results into categories of importance (e.g., fault category, good vs. bad batch, etc.), then use discriminate analysis (DA) in conjunction with the PCA and PLS.
Through the application of data analytics, it is possible for the operator to monitor a batch operation simply by looking at a plot of the PCA statistics and the PLS estimated end-point value for quality parameters, as illustrated in Figure 2.
Figure 2. Operators can monitor a batch operation by looking at a plot of the PCA statistics and the PLS estimated end-point value for quality parameters.
As illustrated in Figure 2, the primary measurements that contribute to a process deviation may be displayed as contribution plots. These plots show how much each process variable contributes to the deviation and, thus, can help to determine the source of a measured or unmeasured disturbance quickly. Thus, when the current batch is evolving, if something deviates from acceptable variation relationships derived from the analysis of past batches, the operations staff may drill down into the process variables to understand why.